Geometry and measures worksheet — GCSE Foundation

1.A scale drawing of a rectangular lawn uses a scale of 1 : 125. On the drawing, the lawn measures 4 cm by 2.4 cm. Work out the perimeter of the real lawn, in metres.

2.Two triangular offcuts of wood, PQR and STU, are cut for a construction project. PQ = 8 cm, QR = 6 cm and angle PQR = 90°. ST = 8 cm, TU = 6 cm and angle STU = 90°. A carpenter wants to check the two pieces are identical in shape and size before using them as a matching pair. Using only the measurements given, and without working out any further lengths, which condition proves that triangle PQR is congruent to triangle STU?

3.Which of these correctly compares a 'line' with a 'line segment'?

4.The diagram shows a solid made from two cuboids joined together. Which shape is the front elevation of this solid?

5.A rectangular name card has a perimeter of 30 cm. The card is 9 cm long. Work out the width of the card.

6.Triangle ABC has AB = 8 cm, angle B = 50° and BC = 6 cm. Triangle DEF has DE = 8 cm, angle E = 50° and EF = 6 cm. Which condition proves the two triangles are congruent?

7.p is the column vector with top number 5 and bottom number 1. q is the column vector with top number −2 and bottom number 3. Work out p − 2q, giving your answer as a column vector in the form (top, bottom).

8.A polygon has 9 sides. What is the name of this polygon?

9.A solid is built from centimetre cubes: a base layer of 2 rows of 3 cubes each (a 3 by 2 rectangle of cubes), with one extra cube placed on top of one corner cube of that base. Looking down from directly above (the plan view), how many squares are visible?

10.Four angles meet at a point. Three of them measure 82°, 105° and 96°. Work out the size of the fourth angle.

11.Work out the exact value of (cos 45°)² + (sin 45°)².

12.A triangular prism has two triangular end faces and three rectangular faces joining them. How many faces does it have in total?

13.Two sides of a triangle are 20 cm and 8 cm long. Write down which one of these lengths is possible for the third side.

14.A solid is built from five centimetre cubes, standing side by side on a table in a single straight row. Looking down from directly above (the plan view), how many squares are visible?

15.Triangle ABC has AB = 5 cm, BC = 7 cm and CA = 9 cm. Triangle DEF has DE = 5 cm, EF = 7 cm and FD = 9 cm. Which condition proves the two triangles are congruent?